Implementation of MADM Methods in Solving Group Decision Support System on
Gene Mutations Detection Simulation
Ermatita
*1, Sri Hartati
*2, Retantyo Wardoyo
*2, Agus Harjoko
*2*1Department of Information System , Computer Science Faculty of Sriwijaya University Indonesia
(Doctoral Program Student Computer Science Gadjah Mada University ) Jl. Palembang-Prabumulih, Ogan Ilir, INDONESIA
1ermatitaz@yahoo.com
*2 Departement of Computer Science and Electronics
Mathematics and Natural Sciences Faculty Gadjah Mada University, Indonesia
Abstract—Detection of gene mutation is an activity that can provide contribution in the medical field. Detection of mutated gene is needed to avoid the diseases caused by them such as cancer. The detection of gene mutations can be performed by utilizing computer-based system. Group Decision Support System (GDSS) is a computer-based system that can be utilized in detecting human gene mutations that cause disease. The ELECTRE method, which is a Multi-Attribute Decision Making, is a method in modeling multi-criteria GDSS. In this paper we propose implementation of model for multi-criteria GDSS in which the simulation data is the mutated genes that can cause cancer.
Keywords: Group Decision Support System, ELECTRE, gene mutation
I. INTRODUCTION
A Group Decision Support System (GDSS) is a computer-based systems to support a collection of groups who have a common task or goal. This system typically provides an interface for users who are the member of the group. The GDSS can accelerate decision-making process or improve the quality of the resulting decisions, or both. This can be done with the support for the exchange of ideas, opinions, and choices in the group on the system. The Group Decision Support System can be applied to the field of information technology which is able to assist in providing decision regarding mutated genes that may or may not cause cancer.
Some alternative methods for the determination of group decision making have been improved by researchers. This method was developed to determine the best alternative from several alternatives based on criterion in making decisions. One of the method in decision making group is Multiple Criteria Decision Making (MCDM). The MCDM is divided into two models: Multi-Attribute Decision Making (MADM) and Multi-Objective Decision Making (MODM). The decision to justify whether the genes affected by genes causing cancer can be done by conducting ranking MCDM ELECTRE method. For that purpose, we need a model in decision-making process to detect the gene mutations that can cause cancer. In this paper, we propose implementation of GDSS Model by using the ELECTRE method to detect gene mutations
simulation in mathlab aplication. This model is made by using a simulation of the some defined criteria.
II. BACKGROUND THEORIES
2.1 GROUP DECISION SUPPORT SYSTEM (GDSS) GROUP DECISION SUPPORT SYSTEM (GDSS) is an interactive computer based system that facilitates solution of some unstructured problems by a few (sets) of decision makers who work together as a group. GDSS can be applied to different groups of decision situations (group), which includes a review panel, task force executive meeting / board, remote workers, and so forth. The basic activities that occurred in any group and who require support on a computer are:
1. Calling information, involving the selection of data values from an existing database or calling simple information.
2. Information sharing, meaning the viewer displays the data on the screen to be viewed by groups. 3. Use of information, including application software
technology, procedure, and group problem solving techniques to the data. [8]
2.2 MULTI- CRITERIA DECISION MAKING
Multi-criteria decision making (MCDM) is the decision-making technique by considering some alternatives options.
The Multiple Attribute Decision Making (MADM), comes to elections, in which mathematical analysis is not needed. This type of MCDM can be used for the election in which there is only a small number of alternative courses. The MADM is used to solve problems in discrete spaces, typically used to solve problems in the assessment and selection of limited number of alternatives.
The MADM approaches are done through two stages, namely:
1. Perform aggregation of the decisions that responds to the decisions corresponding to all destinations on each alternative
According[4]: MADM is evaluated against the alternative m Ai (i = 1,2 ,...., m) against a set of attributes or criteria Cj ( j = 1,2 ,..., n) where each attribute are not mutually dependent with each other. Decision matrix of each alternative on each attribute, X is given as:
⎥
Where xij is an alternative performance rating in relation to the j-th attribute. Weight value indicates the relative importance of each attribute, given as, W:
W = { w1 , w2, w3, …, wn }
Performance rating (X) and weight value (W) represent the core values corresponding to the absolute preference of the decision makers. The MADM problems is finalized with an alternative process to get the best ranking obtained based on the overall value of granted preferences (Yeh, 2002) in [4].[4]
2.3 ELECTRE
The ELECTRE (Elimination Et Choix Traduisant He realite) is based on the concept of ranking by paired comparisons between alternatives on the appropriate criteria. An alternative is said to dominate the other alternatives if one or more criteria are met (compared with the criterion of other alternatives) and it is equal to the remaining criteria. Ranking relations are between two alternatives Ak from the A1 (Roy, 1973) in [4].
The researches on the ELECTRE method has been widely applied, for example:
(Zhang,2004) conducted a study: The ELECTRE method based on interval numbers and its application to the selection of leather manufacture alternatives. In this study, it is studied how to make use of traditional methods for certain circumstances to solve the MADM with interval numbers. The paper proposes an enhanced ELECTRE method based on the number of intervals. This is performed by considering the specificity of interval numbers, using the possibility degree for ranking alternatives, founded the discordance dominance matrix and aggregate dominance matrix, then eliminating inferior alternatives. This method can be used to MADM, where the values of attributes in the form of interval numbers, and solve the difficulties in ranking a number of intervals in the traditional method. The selection of leather-making problem solving with this method, and illustrated its application in real life.
(Bashiri,2009) in his research on MADM methods associated with the decision maker's point of view about the Importance degree of responses. The results given is assumed that the response-means clustering is more important than the standard deviation. Another advantage of this method is it considers the standard deviations that
contribute to the strength of experimental design, because it only uses one appropriate response regression function, so that this method reduces the statistical error. Because this method attempts to obtain a value of several responses, then it can be grouped in the desirability function approach.
(Soultammohammadi,2008), conducted an applied research Analysis by an outranking multi-attribute decision-making technique, called Elimination et choix traduisant He realite method. This approach is applied to an illustrative example where Analytical hierarchy process method applied to calculate the global weights of the attributes of the couple through the comparison matrix. This study shows the proposed AHP-ELECTRE algorithm; outranking relations between the alternatives and in this way, non-dominated sets of land-use alternatives other alternatives can be identified. In this approach, the worst alternative for the examples given can be recognized as well. Results obtained by ELECTRE outranking is better than the TOPSIS ranking. This approach is beneficial especially when the number of alternatives more. This means that, further research is still needed to facilitate decision making MADM tool more appropriate to apply in the field of MLSA.
2.4 ELECTRE METHOD FOR GENE MUTATIONS DETECTION SIMULATION
This paper proposes a modeling of MADM with ELECTRE method to detect gene mutations simulation in humans who suffer cancer. The mutations that might occur is that there is activation of the Rb gene c-myc gene or inactivation of p53 gene. In order to detect whether a person is identified to have cancer cells or not. The data were collected from the study of gene mutations [6]
Table.1 Expression of protein p53,Rb and c-myc
Source (Prayitno,A. 2005)
In this simulation, it can be applied to the three alternatives in the set to the identification of cancer cells in the human gene, namely:
Based on the gene expression in reference [6], there are three which reference in making decisions to detect a person experiencing the gene mutated, namely:
C1 = p53 protein expression (in%) C2 = Rb expression (in%) C3 = c-myc expression (in%)
The suitability rating alternatives on each criterion will be the value of the numbers one to five, namely: 1 = very bad ,2 = bad, 3 = enough, 4 = Good,5 = Very good.
Level of importance of each criterion in value by one to five, namely:1 = very low, 2 = Low, 3 = enough, 4 = High,5 = very high
From the above criteria, a match rating is made for each alternative on each criterion. The rating a match is made by simulation, that in determining the gene is mutated or not that actually fit all the criteria and rating is obtained from the opinions of experts. The simulated suitability rating of each criteria is indicated by the following table [10]:
Table.2 Suitability of each alternative on each criterion
Alternatif Kriteria
C1 C2 C3
A1 4 4 5 A2 4 5 4 A3 4 3 5
The calculation is done with the completion method Elimination Et Choix Traduisant He realite (ELECTRE), which is based on the concept of ranking by paired comparisons between alternatives on the appropriate criteria. An alternative is said to dominate the other alternatives if one or more criteria are met (compared to the criteria of other alternatives) and it is equal to the remaining criteria. The ranking relationship between the two alternatives Ak and A1 are denoted as Ak ® A1 if alternative-k no-one dominates the alternative to the quantitative, thus better decision makers to take risks Ak than A1 (roy, 1973) in [4]. Decision matrix of the simulation above obtained as follows:
4 4 5 4 5 4 4 3 5
Input the crietion on mathlab as follows: Fig.1 Input criterion
Pairwise comparison of each alternative in each criteria is expressed by values (Xij). This value must be normalized to a scale comparable to (rij). This value is calculated with the formula as below:
∑
=
=
m
i ij ij ij
X
X
r
1 2
dengan i = 1,2,...m, j = 1,2...n (1.1)
| x1 | = √42 + 42 + 42 | x3| = √52 + 42 + 52
From the results of calculations using the above formula in math lab :
The result of calculation obtained as the matrix below:
0,57735 0,565685 0,615457 0,57735 0,707107 0,492400 0,57735 0,424264 0,615457
Furthermore, the V matrix is calculated based on the equation:
From the above calculation results obtained by matrix V:
2,886751 1,697056 2,46183 2,886751 2,12132 1,96950 2,886751 1,27280 2,46183
Calculated for the Association of concordance index (Ckl) that shows the sum of weights of criteria, according to the formula;
Ckl = { j |vkj >vij} for j = 1,2,...,n (1.5) The results obtained with this calculation is as follows:
C12 : v11 >v21 2,886751 > 2,886751 V12 >v22 1,697056 > 2,12132
V13 >v23 2,46183> 1,96950 C12 = {1,3}
The same calculation for each Ckl then obtained value of C as follows:
C12 = {1,3},C13 = {1,2,3}, C21 = {1,2}, C23 = {1,2}, C31 = {1,3}, C32 = {1, 3}
Calculating the value set for the matrix discordonce discordonce associated with the attribute is the following:
dkl = { j |vkj <vij} untuk j = 1,2,...,n (1.6) d12 = v11 <v21 2,886751 < 2,886751
V12 <v22 1,697056 < 2,12132 V13 <v23 2,46183< 1 ,96950 d12 = {2 }
With a similar calculation for each element of the set obtained value D:
d12 = { 2}, d13 = {}, d21 = {3}, d23 = {3},d31 = {2},d32 = {2}
ckl concordance matrix elements calculated using the formula :
dkl discordance matrix element calculated using the
formula:
Concordance matrix calculated based on the dominant [10]
elements of the matrix F is determined as the dominant discordance:
⎩ ⎨ ⎧
< ≥ =
d d jika
d d jika g
kl kl kl
, 0
, 1
- 1 1 G = 0 - 1 1 1 -
Aggregation of the dominant matrix (E) showing a partial preference order of alternatives, obtained with the formula in mathlab:
kl kl kl
f
g
e
=
.
2.2)Result of the calculation is matriks above :
- 0 1 - 1 1
0 - 0 0 - 1 ekl = F x G =
0 0 - 1 1 -
- 1 0
=
0 - 0
0 0 -
Result of the calculation on graphic as follows :
Fig.2 Graphic of result the calculation of model
From the above graphic is A2 dominate A1, A2 also dominate A3. In this simulation, which determined the criteria in Group Decision Support System in simulated from existing data. To simulate the model with the ELECTRE method is A2 dominated A1 and A2dominate A3 . This means that in this simulation of the criteria for determining the simulation showed that the activation of Rb more likely to cause cancer.
III.CONCLUDING REMARKS AND FURTHER WORKS
Group Decision-making can assist in decisions made by a group of people. There are some group decision making methods have been developed, and ELECTRE method is one of the method in group decision making that can assist in the decision making process to determine whether a mutated gene can cause cancer or not, based on existing criteria in the gene mutation. This paper proposes the criteria in a for simulation implementation of modeling using ELECTRE method in mathlab. The results from the decisions is based on the determination of criteria for modeling. The determination of criteria for determining whether a mutated gene can cause cancer or do not has to refer to experts in their fields. This paper demonstrates the implementation of modeling to perform the calculation so that the decision can be modelled by using these calculations. This made the modelling flexible in accordance with the criteria established by the experts for decision making, so that the mutated gene for the determination of a person or not the criteria derived from expert opinion in the medical field. This modeling can be used for real life criteria, based on criteria established by the experts.
REFERENCES
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